How does 'local with parent' space work?
It looks like the second bone has a hidden initial transform of 1.0 in the y direction relative to the origin of the armature. So, it is already at 1.0y, and it movies 1.0z with its parent. Those hidden initial transforms are tricky.

EDIT: Oops, in armatures "Local with Parent" uses its position in edit mode rather than a hidden transform like in object mode.